Our goal is to $\textit{efficiently}$ discover a compact set of temporal
logic rules to explain irregular events of interest. We introduce a
neural-symbolic rule induction framework within the temporal point process
model. The negative log-likelihood is the loss that guides the learning, where
the explanatory logic rules and their weights are learned end-to-end in a
$\textit{differentiable}$ way. Specifically, predicates and logic rules are
represented as $\textit{vector embeddings}$, where the predicate embeddings are
fixed and the rule embeddings are trained via gradient descent to obtain the
most appropriate compositional representations of the predicate embeddings. To
make the rule learning process more efficient and flexible, we adopt a
$\textit{sequential covering algorithm}$, which progressively adds rules to the
model and removes the event sequences that have been explained until all event
sequences have been covered. All the found rules will be fed back to the models
for a final rule embedding and weight refinement. Our approach showcases
notable efficiency and accuracy across synthetic and real datasets, surpassing
state-of-the-art baselines by a wide margin in terms of efficiency.

我们引入了一个神经符号规则归纳框架，该框架通过时序点过程模型高效地发现一个紧凑的时间逻辑规则集合来解释感兴趣的不规则事件。我们采用了矢量嵌入来表示谓词和逻辑规则，并通过梯度下降训练逻辑规则嵌入以获得谓词嵌入的最适合的组合表示。为了使规则学习过程更高效和灵活，我们采用了顺序覆盖算法，该算法逐步将规则添加到模型中，并移除已解释的事件序列，直到所有事件序列都被覆盖。在合成和真实数据集中，我们的方法表现出显著的效率和准确性，以较大的优势超过了现有技术基准的效率。

神经符号时序点过程

Neuro-Symbolic Temporal Point Processes

Rules are widely used in Fintech institutions to make fraud prevention
decisions, since rules are highly interpretable thanks to their intuitive
if-then structure. In practice, a two-stage framework of fraud prevention
decision rule set mining is usually employed in large Fintech institutions.
This paper is concerned with finding high-quality rule subsets in a
bi-objective space (such as precision and recall) from an initial pool of
rules. To this end, we adopt the concept of Pareto optimality and aim to find a
set of non-dominated rule subsets, which constitutes a Pareto front. We propose
a heuristic-based framework called PORS and we identify that the core of PORS
is the problem of solution selection on the front (SSF). We provide a
systematic categorization of the SSF problem and a thorough empirical
evaluation of various SSF methods on both public and proprietary datasets. We
also introduce a novel variant of sequential covering algorithm called
SpectralRules to encourage the diversity of the initial rule set and we
empirically find that SpectralRules further improves the quality of the found
Pareto front. On two real application scenarios within Alipay, we demonstrate
the advantages of our proposed methodology compared to existing work.

在金融科技机构中，规则广泛用于欺诈预防决策。本文关注通过在初始规则池中找到高质量规则子集（如精确度和召回率），采用 Pareto 最优的概念，以找到一组非支配的规则子集，构成 Pareto 前沿。我们提出了一种名为 PORS 的基于启发式的框架，并确定了 PORS 的核心是前沿解选择问题。同时，我们对公开和专有数据集上的各种前沿解选择方法进行了系统分类和彻底的实证评估。我们还引入了一种名为 SpectralRules 的新颖的序列覆盖算法变体，鼓励初始规则集的多样性，并经实验证明 SpectralRules 进一步提高了找到的 Pareto 前沿的质量。在支付宝的两个实际应用场景中，我们展示了我们提出的方法与现有工作相比的优势。